Glasnik matematički, Vol. 54 No. 1, 2019.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.54.1.04
Rational sequences on different models of elliptic curves
Gamze Savaş Çelik
; Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey
Mohammad Sadek
orcid.org/0000-0002-2189-5603
; Faculty of Engineering and Natural Sciences, Sabancı University, 34956 Tuzla, Istanbul, Turkey
Gökhan Soydan
orcid.org/0000-0002-6321-4132
; Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey
Sažetak
Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves over k which possess rational points whose x-coordinates are exactly the elements of S. If the size |S| of S is either 4,5, or 6, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of S are realized as the x-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.
Ključne riječi
Elliptic curve; Edwards curve; Huff curve; rational sequence; rational point
Hrčak ID:
220842
URI
Datum izdavanja:
7.6.2019.
Posjeta: 1.136 *